10.1 Deontic meanings presuppose epistemic meanings

In cognitive linguistics the most influential analysis of modals comes from Talmy’s papers on force dynamics, summarised systematically in Talmy (Reference Talmy2000 [1988]).² Talmy makes four connected proposals that are relevant here, subsequently developed by Sweetser (Reference Sweetser1982, Reference Sweetser1990). The first is that force-dynamic concepts, arising in embodied experience, are cognitively primary structures that are recruited in a wide range of lexical and grammatical structures. The second is that force-dynamic structures have a psychosocial interpretation as well as a physical one. The third is that sociophysical force-dynamic concepts are associated with deontic modals. And the fourth is that the deontic modals are ‘basic’ in the sense of being ‘metaphorically extended’ from an experientially physical source. Sweetser modifies and develops Talmy’s force-dynamic account of deontic modals, and places them in a diachronic account of the meanings of English modal auxiliaries, arguing for a historical progression from deontic meanings (more concrete) to epistemic (more abstract) meanings, a claim supported by the work of Traugott (e.g. Reference Traugott1989). Stated in this way the claim is about the historical development of a vocabulary. The more general claim is that the relationship between the deontic and the subsequent epistemic meanings is metaphorical, in the sense of conceptual metaphor theory. The implication (possibly unintended) is that such a relationship is synchronically true also – i.e. that such a relationship is to be found in the semantic description of the synchronic meaning or utterance processing of deontic and epistemic modals. This ought surely to mean that if we seek to describe the conceptual structure associated with epistemic words, deontic concepts are somehow involved, but not vice versa. I do not think that this is the case.

Langacker’s account (Reference Langacker1991: 273–5) endorses and claims to be a ‘refinement’ of Sweetser’s force-dynamic account of modal meaning. However, despite similarities, his account does not appear to take the metaphorical mapping of force onto epistemic modals to be primary. Rather, it appears to offer a basic model in which time and degree of known-ness is fundamental and is characterised by directionality and distance. Importantly, Langacker seems to give primacy to the idea of the speaker ‘as the person responsible for assessing the likelihood of reality evolving in a certain way’, while the force-dynamic element appears to be derivative: ‘the notion of evolutionary momentum [in the sense of a temporally evolving reality] might well engender the conception of the speaker being carried by the force of evidence along a deductive path’ (Langacker Reference Langacker1991: 274). There may be elements in this account that are in line with what DST assumes about the fundamental role of epistemic assessment. However, as far as I can see, it leaves us without any account of deontic conceptualisation as such.

That metaphorical mapping from more concrete to more abstract concepts underlies semantic change is not at issue here. But there is a different problem, one that was not in the focus of the Talmy–Sweetser framework. The problem is that, so far as the synchronic semantics are concerned, deontic meanings appear to presuppose epistemic ones. The connection is not metaphorical but presuppositional. For example, it is awkward, it seems to me, to say John must clean up the mess but maybe he won’t,³ while it is acceptable to say John should clean up the mess but maybe he won’t. This shows not just that must is ‘stronger’ than ought but that both verbs presuppose an epistemic judgement about the action denoted by the complement over which they scope, namely, clean up the mess. On introspection, to make a deontically modalised assertion seems to involve having in mind a representation of a world that is not actual, in parallel with one that is actual. In the parallel world desired or required actions are executed by actors who exist in the actual world, and this parallel world can be imagined as possible, probable or necessary, etc. as well as in varying degrees subject to or free from obligation (however that is defined).

To put these points in a slightly different way, if a speaker S says that her friend ought to do so-and-so, two things are clear about the use of ought: the friend is not doing so-and-so, or not yet; the speaker is invoking some kind of authority, moral duty or practical rule. At least, it would on the most usual understanding be strange to say she ought to be doing such-and-such if she already is, and at least there will be a tacit invocation of a norm, even if that norm is simply what is required in order to accomplish a practical goal. Intuitively, when S says ‘she ought to do it’, the associated conceptualisation seems to involve some imaginary domain in which she does do it simultaneously with a real domain in which she does not. Such mental constructs are not confined to deontic expressions. There are two components here that go hand in hand: counterfactuality and normativity. The normative element can indeed be insightfully modelled as a sort of force, as the Talmy–Sweetser approach does, and as the DST approach is also equipped to do. But counterfactuality is essential to what constitutes deontic understanding and counterfactuality, as proposed in Chapter 6, is essentially a reversal, that is, in geometrical terms, a reflection of the epistemic dimension.

In the accounts of modality outlined above (those of Talmy, Sweetser and Langacker), the term ‘root’ modal has been adopted to place dynamic modality (loosely, to do with physical ability) and deontic modality (to do with obligation and permission) in the same category and epistemic modality in a separate one. The present theory does not adopt this division, since the term ‘root’ is potentially misleading in appearing to already embody a claim of priority, as well as in putting together under the label ‘root’ two types of modality (dynamic and deontic) that can be distinguished (see Palmer Reference Palmer1986: 102–3). And the epistemic dimension in DST is a fundamental cognitive dimension, not a derivative of supposedly more basic cognition. The present account of deontic modals shows why both the epistemic dimension and the category deontic are required.

The approach that is adopted here starts with conceptual space. Rather than examining the lexical expressions first in terms of their interrelations and their polysemy, the aim is to explore the structure of the conceptual space that gives rise to the need for lexically communicated modal meanings in the first place. This is the approach followed by Winter and Gärdenfors (Reference Winter and Gärdenfors1995) in their account of modals and also, more broadly, by Gärdenfors (Reference Gärdenfors2000). The present chapter, then, seeks to outline the structure of deontic concepts, and to do this it uses a geometrical model of conceptual space that is developed in DST, not only for modal concepts but for other conceptual structures too that are communicated via language.

Like Winter and Gärdenfors (Reference Winter and Gärdenfors1995), this chapter also derives an important part of its account of deontic modals from Talmy’s insights concerning force concepts, but does not use them in exactly the same way. Winter and Gärdenfors remain interested in the nature of the etymological shift from deontic to epistemic, which they claim is gradual rather than metaphorical, and they do not focus on a synchronic conceptual relation between epistemic and deontic domains. The DST approach does not treat epistemic modal concepts as ‘extended’ from sociophysical concepts in the sense of some kind of conceptual one-way relation in the mind of a speaker. It is not clear in any case what this would mean. Note that as soon as one formulates the problem in terms of concepts in the mind rather than lexical items the blurring of synchronic and diachronic in the Sweetser account becomes obvious. If we ask what is the nature of the epistemic concept that people have in mind when they use a modal like must or should in an epistemic sense, we need also to ask what it means to say that such an epistemic sense ‘derives from’ or is ‘extended from’ a deontic sense. What I want to look at in this chapter is the structure of the deontic conceptualisation people have in mind when they express it in linguistically available code.

The normative part of this conceptualisation can, as already noted, be modelled in terms of a force-dynamic component: loosely, the sense of compulsion or ‘oughtness’ that is activated by the use of deontic expressions can be explained in terms of a force-dynamic image schema that metaphorically has a source and has impact on an affected participant. In this I do not fully follow Winter and Gärdenfors (Reference Winter and Gärdenfors1995), however, who reduce the deontic source to ‘social power’ existing between speakers in a speech act (see Section 10.3 below).

I have suggested above that deontic conceptualisations probably involve contrasting parallel conceptualisations, one in the actual world, one in a counterfactual imposed world. This view is similar in certain ways to Frawley’s account of deontic meaning as ‘involving two kinds of world’ (Frawley Reference Frawley1992: 420). But the DST account is distinct from Frawley’s in viewing deontic conceptualisation as dependent on epistemic conceptualisation. More fundamentally it is distinct from all approaches in taking advantage of Fauconnier’s theory of mental spaces as a way of understanding the idea that two ‘worlds’ are somehow involved in deontic conceptualisation. But in turn, DST is different from mental-space theory too. DST incorporates Fauconnier’s idea of multiple cognitive spaces and referent mappings across such spaces, but it goes beyond mental spaces in the following ways: DST proposes an essentially deictic grounding for such spaces, it takes the spatial underpinning of many conceptualisations seriously by using geometrical descriptions and it uncovers unsuspected relationships between spaces when viewed geometrically.

The DST framework was not set up specifically to explain deontic modals. An account of deontic modals does, however, come out of it and the reason for this is that, precisely because of its geometrical conception, it intrinsically provides both for multiple related spaces and for directed forces.

10.2 Deontic reflections

The task now is to show how geometrical modelling can be used to model deontic conceptualisations. This might seem a curious notion at first sight but I hope to show that the DST approach can capture a number of interesting dimensions of deontic meanings. In particular, in this section I show how epistemic meanings are part of the conceptual structure of deontic meanings. The essential epistemic component is counterfactuality, and as we have seen, counterfactual conceptions can be modelled as geometric reflections of the base space R. This does not mean the notion of force is irrelevant. Force also an essential ingredient. It is not necessary to introduce any extra machinery to deal with this, as the DST approach already has vectors, which can be interpreted as standing for force directed from a binding source.

10.2.1 First-order reflection of R: obligation

Deontic meanings presuppose epistemic meanings, primarily counterfactual ones. While a clear-cut distinction between epistemic and deontic modality is generally accepted, many of the theoretical semantic accounts make the point that deontic meanings, like directive meanings (for example, Lyons Reference Lyons1977, Langacker Reference Langacker1991, Frawley Reference Frawley1992), involve a non-existent or not-yet-existent or desired or irreal or imposed action or state of affairs. This surely means that the epistemic is interwoven with the deontic in the conceptualisations that arise in the course of producing and understanding deontic utterances. Within the present framework I refer to the mental representations of the epistemically non-real simply as ‘counterfactual’. The type of conceptualisation in question involves the combination of factual (for the speaker S) elements as well as (again for S) counterfactual elements. The geometrical format that DST uses is able to precisely characterise this combination.

We will consider examples such as the following:

(1)

a Mary must write the report

b Mary must not write the report.

The crucial point here is that there is a counterfactual presupposition in (1a) and (1b): that Mary is not at the time of speaking writing (or intending to write) the report, so far as the speaker S knows. At the same time, the sentence leads us (as presumably its utterer wanted) to entertain the notion that in some possible world Mary does write it. This is the basis on which I am proposing the idea of the deontic mirror world. Mary is not doing the desired action in the speaker’s reality but is represented as doing it in the speaker’s ideal or desired world. We need a way of modelling this kind of ideal or desired world relative to the speaker’s real world and we can do it semi-formally as follows. There is a base axis system R, which is real-for-S, and within R Mary is not writing the report. Simultaneously there is another axis system R′, in which Mary ‘is’ writing it. And hearers of (1) mentally represent both R and R′ because of the conventional meaning of the English modal must.⁴

In describing deontic meanings semanticists sometimes talk of the ‘imposing’ of one world on another by some individual or institution with authority or power (see Lyons Reference Lyons1977: 827). Frawley (Reference Frawley1992) speaks of the ‘imposition’ of an ‘expressed world’ on a ‘reference world’. Langacker’s account appears to emphasise a similar epistemic structure (Langacker Reference Langacker1991: 269–81). Force-dynamic accounts use a similar metaphor, but do not speak of this simultaneous dual structure with its differentiated epistemic components.

As we have already noted, there is another component of the deontic meaning of must, namely the concept of some kind of compulsion, resembling the force-dynamic account proposed by Johnson, Talmy and Sweetser. Since DST draws on the idea of vectors, we already have a force concept in the elementary physical understanding of vectors themselves. We shall explore how force vectors can in a natural motivated fashion be combined with insights about the different kinds of ‘reality’ involved in deontic meanings.

The model I am proposing for deontic obligation concepts is built on the same reflection geometry that structures counterfactual conditionals, as described in Chapter 6. The configuration required is repeated in Figure 10.1. We can think of this as representing the fundamental counterfactual space that is apparent both in the kinds of conditional sentences we have examined and in deontic conceptualisations. As we have already noted, this kind of conceptual space superimposes the non-real on the real (for the speaker).⁵ The concept of counterfactuality makes no sense unless both a base world and a counter-world are simultaneously held in mind.

Figure 10.1 Base axis system and reflected copy

The range of obligation concepts facilitated by English modal verbs can be seen to be structured within this double world. In this world the time axis (t) and the referential axis (d) correspond, but the m-axis, the scale running from what is real for S to what is not-real or counterfactual for S, is reversed. So for S′ at the origin of this reflected system R′ what is counterfactual in R is real, and conversely for the counterfactual in R′. The whole reflected space of R′ corresponds to a state of affairs that is desired, or desirable, including ethically desirable. Of course the precise deontic or ethical basis is determined pragmatically, that is, in the interlocutors’ shared expectations, which can include merely S’s desires or some source external to S.

Figure 10.2 takes the fundamental counterfactual configuration of Figure 10.1 and positions vectors within it corresponding to modalised action verbs, in particular, obligation concepts encoded in the lexemes must and should. Various tense forms are considered.

Figure 10.2 Obligation expressions

For example, we consider Mary must not write the report and Mary should have written the report. And we are concerned not only with the deontic meanings themselves but also with the effect of certain tenses that exclude deontic meanings but allow epistemic ones. The sentences we shall consider are listed below. They are variations on (1). The sentences are ambiguous between deontic and epistemic meaning but it is the deontic meaning that is to be assumed here: the starred sentences are those for which a deontic reading is not available without further specification of context.

(2)

a *Mary must be writing the report

b *Mary must not be writing the report

(3)

a *Mary must have written the report

b *Mary must not have written the report

(4)

a Mary should write the report

b Mary should not write the report

(5)

a Mary should be writing the report

b Mary should not be writing the report

(6)

a Mary should have written the report

b Mary should not have written the report.

In Figure 10.2 above the vectors stand for the directed action write, the tail starting at the coordinate for the writer (Mary) and the tip touching the thing written (the report). The writer, Mary, and the report have their labels in R, the coordinate system representing the world as real for the speaker (subject) S, though of course their coordinates run through into R′, since R and R′ are aligned. But the vectors are another matter: they are modalised for S, that is, they may be true, untrue, desired, required, possible, probable, untrue, etc.

Let us consider each of the cases in turn as they are positioned in the dual space configured in Figure 10.2.

10.2.1.1 must + V, must not + V

In example (1) the event of Mary writing the report is understood to be at some time t > 0. While (1) is perfectly normal, the examples in (2) and (3) are not. This follows from the natural conceptual structure of illocutionary acts that would be being performed, were a speaker to use sentence (1) in some plausible context. In more general terms, it also follows from assumptions about causations. That is to say, you cannot cause something to happen in the past. Nor can one impose on somebody the obligation to have done something in the past. Of course, we can say things like John was obliged/had (got) to do X, but this is a report of an obligation that John was under in the past, not a use of this utterance to bring about an action in the past that has not taken place. Moreover, a sentence like (1) requires that we understand the source of the obligation as being the speaker; it is not understood as a report of an obligation imposed by some other person. The use of must in the present tense with second person subject has a pragmatic effect related to that associated with imperative forms understood as commands.

In terms of Figure 10.2, the must + V construction gives a conceptual configuration that can be described as follows. In R′, the reflected deontic world, S′ views reality R from an opposed viewpoint. From this viewpoint, the event of writing referred to in (3a) is ‘real’ in R′, thus positioned at m′ = 0, with tail coordinates at Mary and tip coordinates at the target of the action, the report. The location on the t-axis is at some time t > 0. And t must be greater than zero for the same reason that it cannot be less than zero – one cannot require or command an action that is already taking place at utterance time t = 0. In R, however, it is assumed to be not the case that the writing is taking place. Accordingly, the write vector in R is found at the counterfactual end of the epistemic modal axis m, as required. This result, which follows from the mirror-reflection geometry, corresponds to a large part of the epistemic semantics that is incorporated in the deontic semantics of must.

Consider now (1b), Mary must not write the report. At the distal (counterfactual) end of m′ in R′, i.e. at what is the opposite of what S demands in the deontic space – is located an act of writing. Simultaneously, there is an assumption that Mary will, contrary to what S requires, write the report in R.⁶

Now (1b) and its geometric representation correspond to a prohibition, and in Section 10.2.2 below we shall use this point in order to build a representation of deontic prohibition and permission modals. A consequence is that the obligation scale and the permission scale are not, pace Frawley (Reference Frawley1992: 422), totally unrelated to one another; in fact, they seem to be conceptually entangled in certain ways that will be discussed below. For the moment it is important to point out that m′ in R′ corresponds to commands at m′ = 0 and prohibitions at m′ = counterfactual (irrealis).

10.2.1.2 must be V-ing, must not be V-ing

The construction with present progressive clearly does not behave in the same way as the must with bare infinitive. In Figure 10.2, examples (2a and b) and (3a and b) are starred because they are not acceptable on a deontic reading. The sentence Mary must be writing can only express S’s epistemic assessment of the degree of truth of the assertion that Mary is writing – viz. that it is highly probable that the activity is occurring. For this the relevant DST diagram would not involve reflected axes, merely the base system, which already incorporates an epistemic scale, viz. the m-axis. It is true, of course, that a deontic reading can be imagined for must (not) be V-ing, but a special context is needed, one which embeds this construction in a future event. Thus for a deontic interpretation of (2) we have to invent a context like: Mary must (not) be writing the report when the boss comes in. The progressive in this reading is relativised to some future time (when the boss comes in) relative to S.

If the progressive is given a present time reading relative to S, the only interpretation is epistemic. This is consistent with the fact that deontic modalisation can only apply to events viewed as taking place at some t > 0.⁷ If we put event e at t = 0, then the meaning is limited to the epistemic meaning. Conversely, we cannot make the epistemic reading of must + V apply to a future event e at t > 0. The strong epistemic modal must applies only to events at t ≤ 0. The reason is noted by many commentators: it is only present or past events about which we make a strong epistemic judgement about the probability of their occurrence, while future events are inherently epistemically uncertain. This means that weakly predictive Mary may_epistemicwrite the report next week is acceptable with reference to a future event of writing, but strongly predictive must_epistemic is not acceptable in this construction.

However, we can have a future reference for the following progressive construction with must as epistemic: Mary must_epistemic(not) be writing the report next week. Nonetheless, it is arguable that must in such expressions relates to an inference carried out by the speaker at a time coinciding with utterance time. The time of the event can, as in (5), be tied to the future by way of the time adverbial. Equally it can be tied to the utterance time in the same manner: e.g. Mary must (not) be writing the report at the moment.

Further, it is worth noting that when the natural conceptual constraint prevents the deontic reading of must for present time points, the epistemic meaning comes up as a default. This may be a corroboration of DST’s assumption that the epistemic scale m is fundamental, not a derivative, at a conceptual level, of deontic meaning.

10.2.1.3 must have V-ed, must not have V-ed

The cases (3) follow the same pattern, mutatis mutandis, as (2) and for the same reasons, namely, that the conventional meaning of must is linked to illocutionary pragmatic force of a quasi-causal nature and thus cannot apply to a relation between present utterance and an event e_{t ≤ 0}. When we turn to should, however, the situation is somewhat different.

10.2.1.4 should V, should not V

In cases (4), it is required that the future event is at t > 0, as for must in (1). How then does should differ in meaning from must? Whereas for must there is (it seems to me) a counterfactual inference connected with must in (1), this is not so obviously the usual interpretation for (4). We can, for instance, have the following:

(4′)

a Mary should write the report and she will / Mary should write the report but she won’t

b Mary should not write the report and she won’t / Mary should not write the report but she will.

The assertion that Mary should (not) write the report can be overridden by its negation by the same speaker. This does not work for must. Taking another look at (1), we have:

(1′)

a Mary must write the report and she will / ? Mary must write the report but she won’t

b Mary must not write the report and she won’t / ? Mary must not write the report but she will.

In using must, it seems that the prompted conceptualisation (and the speaker by implication) does not admit the possibility of non-compliance or contradiction. The assertion that Mary must (not) write the report is questionably compatible with its contradiction by the same speaker. This rather subtle difference corresponds in part with the difference in meaning between English must and should.⁸

In addition, a word such as maybe is compatible with should but not must:

(4′′)

a Mary should write the report and maybe she will / but maybe she won’t

b Mary should not write the report and maybe she won’t / but maybe she will.

With should, the prompted conceptualisation seems to accept indeterminacy. But not so in the case of must:

(1′′)

a Mary must write the report ?and maybe she will / ?but maybe she won’t.

With must, taking the speaker as deontic source, epistemic uncertainty about the required event is not entertained.

In terms of the DST format, these points suggest that the construction should/should not V is located at the medial point on m, as it is in Figure 10.2. In saying ‘Mary should write the report’, a speaker is not necessarily presupposing that Mary is not writing the report: accordingly, Figure 10.2 does not show any instance of the should vector at the counterfactual end of the m-axis in R or at the factual end for should not. This situation is, however, slightly different for the present progressive and present perfect constructions.

10.2.1.5 should/should not be V-ing and should/should not have V-ed

A further important property that distinguishes should from must is the difference in the way the two English auxiliaries interact with aspect and tense meaning. Differently from the must construction, a deontic reading is available for the progressive aspect (5) construction and for the present perfect construction (6).

First, the present progressive and the present perfect tolerate deontic interpretation. This implies that the deontic semantics here do not, unlike those for must, include quasi-causal illocutionary force. They are not used in order to bring about some action; rather, they are used to pass judgement (with respect to some norm) on the doing or not doing of some action, whether or not these actions are viewed as present, past or future.

Second, though we cannot compare directly with must (since must has no deontic meaning for progressive and perfect constructions), it is worth considering whether there are counterfactuality inferences for should in sentences such as (3) and (4):

(3′)

a Mary should be writing the report and she is / but she isn’t

b Mary should not be writing the report and she isn’t / but she is

(4′)

a Mary should have written the report and she has / but she hasn’t

b Mary should not have written the report and she hasn’t / but she has.

Although I think the default, on hearing ‘Mary should be writing the report’, is to assume that she is not (i.e. to add ‘but she isn’t’ is unproblematic), ‘Mary should be writing the report and she is’ does not seem impossible; certainly it is more acceptable to my mind than (1′).⁹ Something similar seems to be the case for should/should not have V-ed. It is also important to note that maybe also seems to be within the limits of acceptability for (3) and (4), as it is for (2). The situation for the progressive and the perfect constructions thus seems to be different from that of the should + V construction. They are both compatible with inferences that a reference event has, has not or merely may have taken place, and that such an event is, is not or may be taking place. This is not the case for future events, since only maybe can be asserted for future events in R.

10.2.2 Second-order reflection: prohibition and permission

Deontic meanings are inherently more complex than epistemic ones because they imply and interact with epistemic meanings. The geometric approach seems to be an elegant way of capturing the complexities. Though this does not mean the diagrams are simple, they are systematic. In standard accounts of modal expressions, not only for English, the concepts of prohibition and permission are treated as members of the deontic category. The question that now arises is whether they can be modelled in the kind of integrated theory of modal concepts that DST attempts to build.

Frawley (Reference Frawley1992: 422) insists that obligation and permission are on two separate, non-overlapping scales. This seems to be true up to a point but the two scales (corresponding to the two worlds of obligation and permission) are clearly in some sort of relationship one to the other. To make sense of the conceptual relationship, permission needs to be defined by reference to prohibition. Prohibition can be regarded as the issuance of an obligation to not-p, e.g. Mary must not write the report. In part, prohibition appears in the obligation deontic world that we have been exploring so far. I say in part, because you must not do p is significantly different from you may not do p. Nonetheless, these two sentences are in practice prohibitions, despite the conceptual difference.

The difference has to do with the fact that obligation is imposed on the real world R while permission is imposed on the obligation world R′. The presumed background to permission-giving is the obligation to not do p. This is why, in Figure 10.3, permission emerges as a mirror transformationR′′ of R′. That is to say, the permission world is a reflection, or reversal of R′, which brings it into alignment with R. Note that this does not mean it is the same as R, since all transformations are copies of R that remain in the DSM in their own right, as a kind of conceptual ‘background’. If we appear to be just going back to where we started, that is what we need, because for one thing R is the world of fact that is resumed, as it were, once the ‘imposed’ worlds are lifted and for another thing we can see how we got there through ideal mirror worlds and their removal. From now on I shall refer to R′ as the ‘obligation space’ (‘O-space’) and to R′′ as the ‘permission space’ (‘P-space’). Every event (vector) that is located in O is an obligation (positive, negative or medial); every event (vector) in P is a permission (positive, negative or medial).

Figure 10.3 Permission and exemption: example (8)

The permission world throws a different light on (1b), which can be understood in two ways, as shown informally in (7) corresponding to (1b) above):

(7)

(i) Mary must not-write the report (i.e. it is the case that Mary must not write the report)

(ii) Mary not-must write the report (i.e. it is not the case that Mary must write the report).

The first of these (i.e. 7(i) corresponding to one reading of (1b) above) can be regarded as prohibition. The second of these can be called ‘exemption’ (Lyons Reference Lyons1977: 773, 837–40). The sentence 7(ii) is not of course a natural English sentence but a way of representing a conceptualisation of what would more naturally be expressed as ‘Mary need not write the report.’

Turning to the P-space created by the transformation yielding R′′, the expressions we are concerned with are the following:

(8)

a Mary may write the report

b Mary may not write the report

(i) Mary may not-write the report

(ii) Mary not-may write the report.

Of examples (8), (8a) and (8b(i)) can be epistemic or deontic but (8b(ii)) can only be deontic. The progressive and perfect forms follow a different pattern:

(9)

a Mary may be writing the report

b Mary may not be writing the report

(i) Mary may not-be-writing the report (if the boss comes in, it doesn’t matter)

(ii) Mary not-may be writing the report (I don’t want the boss to see her writing it).

Of these examples (9a) can only be deontic if the event is relative to a time point in the future relative to S. However, as in the examples in (8), (9b(i)) can be both epistemic and deontic, while (9b(ii)) is deontic only.

As for the following, none of them can be deontic:

(10)

a Mary may have written the report

b Mary may not have written the report

(i) Mary may not-have-written the report

(ii) Mary not-may have written the report.

None of them can be deontic, for the same natural reason that governs present perfect deontic must (though not present perfect deontic should) – viz. that permission cannot be given for a past event or non-event to be enacted if it already has been (or has not been).

Let us now see how these meanings are produced by the mirror–mirror transformation that yields the permission space R′′. Recall that this transformation sets up a reflection of the obligation space or R′. The result of this can be thought of as the reversal of the m-axis. The setting up of the P-space can be also thought of as the ‘lifting’ of obligations, whether positive ones (akin to orders) or negative ones (prohibitions). We illustrate this for case (8) in Figure 10.3.

In the P-space, S is the source of a representation which entertains the scenario of Mary writing the report. We understand may as setting up such a mental space: a world in which Mary’s writing the report is conceptualised as taking place against the presupposed backdrop of the O-space, the space in which S represents the scenario of Mary’s not writing the report.

Consider the extreme points of m′′, the m-axis of R′′, the P-space, in Figure 10.3. The point at m′′ = counterfactual coincides with m′ = 0 (i.e. what S wants to be real in O) and with m = counterfactual (i.e. what S regards as really untrue in the base space R). In other words it is presupposed in R that Mary is not writing the report. In R′ (i.e. the O-space) S conceptualises a world in which she will write it. In R′′ (i.e. the P-space) the entire axis system is in turn reversed (reflected) and the obligation is dissolved. Thus at m′′ = counterfactual we have something like it is counterfactual that Mary must write the report (or in more logic-oriented terms, Mary not-must write the report). This corresponds to (8b(i))Mary may not-write the report or in other words Mary is permitted not to write the report – more naturally expressed as ‘Mary need not write the report, is not obliged to write the report, is exempt from writing the report, etc.’ This position (i.e. m′′ = counterfactual) in the DSM thus represents the complex conceptual structure of an ‘exemption’. In general, P presupposes O and O presupposes its reflected ‘opposite’.

At m′′ = 0 we have a different effect. The prohibition Mary must not write the report is represented in R′ (i.e. in O), where it is located at the counterfactual end of m′. But this point coincides with m′′ = 0, what is entertained as real in the second-order reflection R′′ (i.e. P). What does this represent? It represents S’s conceptualisation of the event of Mary’s writing the report occurring in a conceptual space of permission – in which a presupposed prohibition, which in turn presupposes its reflected opposite (i.e. Mary is conceptualised as intending to write the report in R), is being lifted. Just as the O-space entertains what S desires to impose, so the P-space entertains the lifting of the prohibition. In other words, in P the speaker S is representing the occurrence of the event of Mary’s writing the report: Mary may_deonticwrite the report and she will. However, there is some conceptual indeterminacy here, for S may not be expecting with epistemic certainty that Mary will write the report if S lifts the prohibition (i.e. gives permission): Mary may_deonticwrite the report – possibly she will in fact do so, possibly she won’t. The DSM should then also show a vector in P at m′′ = 0 = midpoint, as also shown in Figure 10.3. What is interesting about this is then that deontic may coincides with its epistemic meaning, as we need, given its polysemy.

What the diagram thus shows us is that conceptualisations in P have two ‘background’ conceptualisations, or two kinds of conceptual space. One is the O-space in which there is represented the prohibition Mary must not write the report. The other is the R-space, where S knows what is happening in his/her real world and this includes the idea that Mary will engage in writing the report at some point in the future relative to S. This configuration thus matches the linguistic intuition that understanding (8a)Mary may write the report raises the notion (i) that there is a will on Mary’s part to engage in the action and simultaneously raises (ii) the notion of an obligation to refrain from, that is a prohibition on engaging in the action in question, and (iii) the conceptual reversal of the obligation, where it is imagined that Mary will or might perform the action. In this kind of model, then, permission is a complex conceptual structure which rests on conceptualise obligation which in turn rests on a conceptualiser’s assumptions about his reality.

There remains the question of the meaning of Mary may not write the report suggested in (8b(ii))Mary not-may write the report, in which the permission-giving meaning of may is counterfactual (there is no permission to do x), which is tantamount to a prohibition.

If we compare (1b)Mary must not write the report and (8b) in the sense of (8b(ii)), both can be understood as prohibitions. This is an apparent problem for Figure 10.3, since Mary may not write the report might be expected, qua prohibition, to appear at the counterfactual end of m′′, but because it seems conceptually similar to Mary must not write the report we might also expect it to coincide with the latter. One might argue that this is only a problem if we assume that the may form has to remain in P. In fact, of course, may is polysemous and can appear in O – which is the solution proposed here. Nonetheless, though they are logically and conceptually similar, there does seem to be some semantic difference between the two prohibition forms must not and may not.

There is perhaps another way of approaching this problem. Note first that must-prohibitions (Mary must not write the report) do not have the conceptual form Mary not-must write the report: it is the writing of the report that is entertained counterfactually not the deontic force that is negated. By contrast, the may-prohibitions have the conceptual form, as we have seen, Mary not-may write the report. That is to say, in the latter case, we can regard the entire P-space (the coordinate system R′′) as being reversed (as undergoing yet another reflection transformation) producing a third-order space R′′′. Now, complicated as it may seem, this does have interesting results, as the DSM in Figure 10.4 suggests.

Figure 10.4 Conceptual structure of may-prohibition: removal of prohibition

What we have in Figure 10.4 is a complex configuration of conceptual spaces in which (i) S takes it as real in R that Mary is intending to write the report, (ii) conceptualises an obligation world R′ (that is, O), in which Mary’s intention is reversed (it is ‘real’ in this O-world), (iii) O is reversed to give R′′ (i.e. the P-world) in which obligations are reversed and permission is granted, (iv) P is reversed to give R′′′ and it is here that permission is withdrawn. The difference between must-prohibitions and may-prohibitions then emerges: may-prohibitions withdraw permissions. May-prohibitions sit on top of permissions, which sit on top of obligations, which reverse the real-world expectations. Note also that we get an alignment between the may-prohibition in R′′′ and the must-prohibition of R′′, which is desirable since it helps to capture the conceptual similarity between the two. In the process of stacking up these copied reflections the conceptual content of each new space (coordinate system), at least for English deontic modal conceptualisations, seems to become less dense and more rarefied, and this is perhaps not unexpected. Indeed it is possible that this is the reason why may not prohibitions, once having appeared in English, have tended to become rarer in use.

10.3 The deontic source

So far I have attempted to model deontic English models in terms of essentially epistemic contexts. What of the force-dynamics account of modal concepts? First, it is worth formally stating a few obvious points about conceptually represented force and actual force in the physical and social world of action.

It is important to distinguish the conceptual representation activated by must constructions from their pragmatic effect. In the conceptualisation, there is an ideal normative counterfactual R′ relative to S in which S or some other source is represented as ‘putting pressure’ on some discourse referent d_i, causing a represented action in R′. No such action has been physically performed at the point when a speaker utters a linguistic expression that conceptually represents it. In the conceptual representation such an action is conceptually counterfactual in R′ and also counterfactual in the physical world in which S utters the utterance. But of course the intention of S in performing the utterance is to ‘put pressure on’ the hearer and in some sort of social pragmatic chain ultimately on Mary. This may (or may not) lead to her carrying out the desired action.

Let us now consider how force is modelled in the relevant DSM. The important point here is that we do not need to add any further formal apparatus. The DST framework already includes the geometrical concept of vectors, and vectors can be conventionally understood as ‘force’, in the metaphorical sense of Talmy, Sweetser and Johnson. Using the geometrical vector notation, rather than ad hoc pictures, is justified since metaphorical force has physical force as its source image schema, and physical force can be conventionally modelled in the sciences and applied sciences in terms of geometric vectors. In this sense, the adoption of the geometric framework of vectors in coordinate systems is arguably well motivated.

Now in the conceptual representation modelled in DSMs, and in the real sociophysical world, the source of the ‘pressure’ can be S or some other source in some other conceptual ‘location’ in the DSM. In the latter case the identity of the source is understood pragmatically among participants in the utterance event. If we wish, we can draw a DSM with a distal coordinate for, say, The Law, Tradition, God, etc. There is another kind of source that can be linked to constitutive rules and Wittgenstein’s idea of games as well as ad hoc tasks-in-hand: ‘in chess pawns are not allowed to move backwards’, ‘if you are writing a paper it must have a conclusion’, etc. But it is not necessary to pursue this point here. All these kinds of deontic sources are complex cognitive frames and scripts that are not part of the semantics per se of must. However, such deontic sources belong to a cognitive frame invoked or presupposed in joint communicative action, though not always explicitly.¹⁰

In this analysis there are some significant differences in relation to Winter and Gärdenfors (Reference Winter and Gärdenfors1995), who reduce deontic meaning to ‘social power’. The problem with this proposal is that, while deontic modals clearly have the potential to be used by powerful social actors, it is not difficult to imagine situations where neither the power of the speaker is evident nor can the sanctioning source the speaker may be indicating be always be treated as ‘power’ – at least without a very general definition of power. For instance, moral principles do not have to be treated as power sources, at least not in the sense of ‘social power’, without long and substantial disputation. The range of possible normative sources that a speaker may invoke is indeterminate. Rather than seek to specify the source of deontic force, the DST model simply assumes a deontic source δ, for δέον, deon, ‘that which is binding’.¹¹ Some δ is always presupposed in deontic conceptualisations. It is a very abstract concept and it is of some interest that such an abstract generalised ‘moral imperative’ is coded into presumably all languages.

But what concerns us here is a more technical matter: how to incorporate ‘force’ into deontic DSMs. Relating the deontic source δ to events in O is a relatively simple matter, given the use of vectors in DST, since vectors are readily interpretable as kinds of causal force and are in any case already needed for modelling causative verbs (cf. Wolff and Zettergren Reference Wolff, Zettergren, Gray and Schunn2002; Chilton Reference Chilton2005). Figure 10.5 gives an idea of how this can be done.

Figure 10.5 Example (1a) Mary must write the report

The proposal here is that a vector f representing moral force, a metaphorical concept, has its starting point at some deontic source. This may be S, as shown by force vector f, or some source distant from S, as shown by force vector f₂. The head of such vectors applies the modal force to a particular discourse entity, which is here the source (Mary in our example) of the action or event (write) in the DSM. What the DSM thus represents is a deontic force acting on Mary and causing her writing of the report. This configuration models the conceptualisation according to which δ or S is in some way the causal agent of the desired action. Figure 10.5 shows two deontic force vectors for illustrative purposes. Either is possible in understanding sentence (la), but it seems unlikely in practice that two denotic sources would appear in the same DSM, perhaps because divided moral authority is not conceptualised.

In this model of deontic force in an epistemic universe, the modal force vector does not simply set up the reflection coordinates O, it represents a quasi-causal force resulting in Mary carrying out the action in the desired (but counterfactual) world O: the source is real, however, and so is Mary who has coordinates that are labelled in R. All coordinates in DST carry through from R into other embedded coordinate systems. As Lyons (Reference Lyons1977: 791) puts it: ‘We can also carry out the psychological process of trans-world identification across real and imaginary worlds of various kinds.’ What we are modelling, then, in Figure 10.5 is a vector that carries force across to a desired counterfactual coordinate space, in which Mary still has a coordinate point on d′.

We might ask: how should we consider the deontic force with regard to the second-order reflection coordinate space P? Does it disappear with the reversing of obligation? The vector modelling does not lead to this conclusion. The force vector f remains, and this seems to be appropriate, for even when permission is granted and obligation is reversed, the prior existence is assumed of the initial imposing of obligation (the deontic force f).

It is important to note that the DSM in Figure 10.5 does not represent a real-life speaker applying illocutionary force on a real-life hearer. Rather it represents what the communication participants have to jointly represent mentally as a consequence of the form of the utterance, whether or not, for example, Mary does in reality write the report in response to what S utters.

10.4 Thoughts on ought

An implicit claim of this chapter has been that the epistemic aspect of conceptualisation is in some way prior to the deontic. What is being tested here is the idea that deontic meanings do in fact presuppose epistemic meanings of the kind we have modelled on the m-axis. As it happens, this idea follows from the way the three-dimensional space of DST is initially set up. But it was not set up for the purpose of arguing that epistemic meaning is prior to deontic; it is independently motivated and it explains a wide range of linguistic conceptualisations. What I have done is try to see what happens if we try to model deontic meanings in terms of DST assumptions, and the resulting analysis is, I believe, logically (and conceptually) consistent within itself. This is not to say that the force-dynamic account is absent from the story of deontics in DST, though it is not used to account for epistemic concepts in the way in which deontic ‘force’ is used by some cognitive linguists to account for epistemic meanings. It seems entirely plausible to think of deontic meaning in terms of some sort of force concept. This proposal is also already present in the DST framework in the form of vectors viewed as force. It is also worth noting that vectors are indeed also part of our account of epistemic meaning, vectors viewed as position markers relative to S, since that epistemic certainty/uncertainty may be related to spatial closeness or remoteness.

The DST model of deontic meaning is not simply a formalised redescription of what has already been said in the semantic literature, including the cognitive-linguistic literature, but carries some fundamental new claims. The most important aspect of the DST account of deontic expressions concerns the epistemic, specifically the counterfactual, dimension. The epistemic dimension, rather than the deontic dimension, is taken to be fundamental. In fact, it is taken to be fundamental to all conceptualisations associated with linguistic expressions. The three dimensions of the basic DST integrate the dimensions of language-linked cognition that approximate to Langacker’s notion of ‘grounding’ (Langacker Reference Langacker1991: ch. 6). Any utterance presupposes that the conceptualiser takes a position with respect to perceived time, relative salience of entities attended to and degree of realness. Langacker refers to the latter as ‘epistemic distance’. And this is precisely what DST attempts to model in a precisely spatial manner.

Where does this leave the Sweetser account which views epistemic meanings as metaphorical projections of prior ‘root’ meanings? There are a number of issues that need to be addressed and I shall only outline them for further reflection. The first point to consider is that the classic force-dynamic account is cast in diachronic terms and need not be a cognitively accurate picture of conceptualisation of deontic and epistemic modality in the adult human speaker. Even as a diachronic account the force-dynamic model makes best sense only in relation to lexical change, for we have no grounds to suppose that speakers in some early phase of a language-using culture first had only deontic concepts and expressions and no epistemic ones, only later acquiring epistemic conceptualisations and expressions. We might argue that such a culture did not much use epistemic expressions in its communication and only in a relatively late phase came to need epistemic expressions derived from its earlier deontic ones: but there is no real warrant for that assumption and little if any discussion of the point. Second, evidence is often adduced from first-language acquisition studies that seem to indicate that English-speaking children acquire deontic expressions before epistemic one. Doubts have been raised about the relevance of these findings (Papafragou Reference Papafragou1998, Livnat Reference Livnat2002, Papafragou and Ozturk Reference Papafragou, Ozturk and Botinis2006). Moreover, it is not necessary to conclude that the order of acquisition confirms a supposed priority of deontic cognition over epistemic cognition in the adult cognitive system underlying the use of linguistic expressions.

In any event, the DST account that I have presented is not incompatible with the force-dynamic one, in particular because force itself is naturally incorporated in the vector geometry of DST and is required for the modelling of deontic source, which is inevitably invoked in deontic expressions. What is distinctive about the DST analysis, however, is the claim that it makes for the complex conceptual interplay between epistemic and deontic ‘worlds’.

Premack and Premack (Reference Premack, Premack, Hirschfeld and Gelman1994) argue that the form of moral beliefs can be distinguished from their contents and set out to establish this form on the basis of observation and experiment with young children. They propose ‘[t]hat just as there are primitives from which one builds sentences so are there primitives from which one builds moral beliefs’. These primitives do not affect the content of either a sentence or a moral belief, but the form. Thus, ‘while the content will vary widely over cultures, the form will not’ (Premack and Premack Reference Premack, Premack, Hirschfeld and Gelman1994: 161). Their view of the content is relativistic and the content seems to consist mainly of what one might call ‘customs’ rather than ethical principles. But it appears that they regard the ‘form’, consisting of ‘primitives’, as universal. ‘The primitives are: intention; positive/negative (right/wrong); reciprocation; possession; power and group’ (Premack and Premack Reference Premack, Premack, Hirschfeld and Gelman1994: 161). The point here is not to argue with these specific claims (though one might want to do so), but to take note that Premack and Premack themselves point out that the primitives do not contribute to the explication of the concept of ought, a concept that many philosophical treatments of morality treat as an irreducible primitive. They put forward the idea, however, that children’s moral ‘primitives’ have the logical form of an ‘expectancy’.

There are some similarities but also some important differences between this approach and the theoretical analysis I have offered in this chapter. It is not clear, for one thing, that studying children’s moral concepts tells us much about adult moral concepts, although Premack and Premack seem to assume, in their concluding remarks, that this is the case. As I have already noted, the DST approach is concerned with the logical form of the adult conceptions that are associated with words like ought. In common with Premack and Premack, the DST analysis does indeed propose a universal form but not content. As to the content, my own view is that this is a matter for philosophical ethics and that universal ethical principles are not excluded. But so far as cognitive linguistics is concerned, what analysis of must, ought, should, etc. tells us is that ought concepts (i.e. deontic concepts) are dependent on epistemic ones, specifically counterfactuality, and that simultaneously they are dependent on a source of ‘deontic force’. Such a source need not be linked with social power. That is, the content of morality need not be reduced to kinds of social power as appears to be done: it is possible for the mind to have a sense (concept) of ought as a special kind of impulsion whose source is nameless. Nor need ought be reduced to ‘expectancy’. What is central is the link with the envisioning of an alternative world.